That second one – critical reasoning skills – is why a lot of students who are good math students in school don’t do as well as they think they will on the SAT Math sections. You might be used to seeing math concepts tested in a pretty straightforward way at school. Well…buckle up because the SAT doesn’t really do straightforward. This test is really good <\/em>at making hard questions out of easy math. <\/p>\n\n\n\n It’s important to brush up on all of your math concepts, but it’s equally important to do a lot of real SAT math practice questions, so you get used to the type of questions you’ll see on test day and improve those reasoning skills! <\/p>\n\n\n\n Top scores don’t just happen from cramming all the math you’ve ever learned. The fact is, the College Board, who creates the SAT, has a lot of documentation on exactly what is “fair game” to be tested. (Don’t worry, we’ll get to this list of of “fair game” topics down below.)<\/p>\n\n\n\n Maybe you’re reading this and you have a few years before you need to buckle down and get serious about taking the SAT, but most likely, the SAT test date is set and you have weeks or maybe a few months to prepare. <\/p>\n\n\n\n Think of this as your study guide for the Heart of Algebra section of SAT Math.<\/strong><\/p>\n\n\n\n Let’s back up for a second. The SAT has two math sections: Section 3 and Section 4 of the test. <\/p>\n\n\n\n These two sections include questions that fall into four categories as defined by the SAT’s College Board:<\/p>\n\n\n\n The Heart of Algebra makes up 30% of the math questions you’ll see on the SAT. That works out to 19 questions total – including both multiple choice and open response.<\/p>\n\n\n\n As you work through the two Math Sections, you’ll notice that the questions start getting more difficult. This is normal. This is also true for both the multiple choice and the open response questions, and, this pattern repeats itself on Section 4. <\/p>\n\n\n\n You’ll find questions that fall into the Heart of Algebra category throughout both Math sections. Easier Heart of Algebra questions will be at the beginning, and as you progress through the rest of the multiple choice, you’ll start seeing more difficult questions. It’s all about the complexity of the question – not just the core concept that’s tested. Remember – the SAT is really good <\/em>at making hard questions out of easy math. <\/strong><\/p>\n\n\n\n It can be helpful to consider this pattern and consider how you pace yourself throughout the Math sections. You may need more time per question towards the end of the math sections. <\/p>\n\n\n\n In this guide, we’re going to look at the Heart of Algebra category of questions. The Heart of Algebra focuses on topics you likely covered in Pre-Algebra or Algebra 1. As you move through the other core math topic areas, you get to more advanced math topics. In the SAT Heart of Algebra section you’ll find questions testing your understanding of:<\/p>\n\n\n\n It may have been a while since you’ve solved linear equations. Maybe you’re a little rusty? Not to worry! Let’s start by understanding more specifically what you need to be able to do to score well on Heart of Algebra questions.<\/p>\n\n\n\n 1. [Linear Equations]<\/a><\/span> Solve, simplify, or interpret linear expressions or equations in one variable. <\/strong>Linear equations look something like this:<\/p>\n\n\n\n Notice that I also said linear expressions<\/em>. Expressions and equations are very similar, but expressions won’t have an equals sign. So, on the SAT, you may see an expression like this: <\/p>\n\n\n\n In one variable <\/em>simply means the expression or equation contains only one variable. In the examples above, that variable is x. Expressions or equations you work with on the SAT may require multiple steps in order to simplify or solve for the variable. They could be pretty straightforward, or more complex, multi-step problems.<\/p>\n\n\n\n If you’re asked to solve a linear equation, the equation may have no solution, one solution or infinitely many solutions.<\/p>\n\n\n\n 2. [Linear Inequalities]<\/span> <\/a>Solve, simplify, or interpret linear inequalities in one variable.<\/strong> Linear inequalities look something like this:<\/p>\n\n\n\n One side does not equal the other. Instead of an equal sign (=), we have greater than (>) or less than (<) signs to work with. While linear equations give us one distinct answer like x = 5, linear inequalities give us a range <\/em>of where our answer can be found.<\/p>\n\n\n\n Again, multiple steps may be required on the SAT in order to simplify or solve for the variable in these inequalities.<\/p>\n\n\n\n 3. <\/strong>[Linear Equations] <\/a><\/span> Create a linear function that models a linear relationship between two things. <\/strong>Moving on from expressions and equations, we arrive at functions. <\/p>\n\n\n\n These types of questions may involve using two variables or function notation to model the relationship described in the question. A function looks something like this:<\/p>\n\n\n\n A function describes a relationship – a relationship between x and f(x). You can plug in any value of x into a function and get a result. This result is your f(x). For the SAT, you need to fundamentally understand how functions can be used and <\/em>how to come up with a function based on given information about a relationship between two things.<\/p>\n\n\n\n 4. [Linear Equations]<\/span> <\/a>Solve, simplify, or interpret linear equations in two variables. <\/strong>This is just like #1, except now we are dealing with two variables. You need to be able to analyze a system of linear equations and understand the constraints between two variables.<\/p>\n\n\n\n If you’re asked to solve a system of linear equations, the system may have no solution, one solution or infinitely many solutions. <\/p>\n\n\n\n 5. [Linear Inequalities]<\/span> <\/a> Solve, simplify, or interpret linear inequalities in two variables.<\/strong> This is just like #2, except now we are dealing with two variables. You need to be able to work with an inequality that contains two variables as well a systems of inequalities. <\/p>\n\n\n\n 6. [Linear Equations]<\/a><\/span> Understand the relationship between a particular context (i.e. real-world scenario) and linear functions. <\/strong>These are those dreaded word problems. You’ll need to be able to make connections between the real-world context and the linear equation that models the context. You may be asked for the meaning of a constant term, a variable, or a feature of an equation.<\/p>\n\n\n\n 7. [Graphing Linear Equations]<\/a><\/span> Understand connections between algebraic and graphical representations<\/strong> of linear equations. You’ll need to be able to:<\/p>\n\n\n\n If you want to maximize your SAT Math score, make sure you understand – and have practiced – questions that fall under each of the above seven sub-categories in the Heart of Algebra section.<\/p>\n\n\n\n We’ve covered the general topics you should know within the Heart of Algebra on the SAT Math, but now let’s take a look in more detail at each of main areas: linear equations, linear inequalities, and graphing linear equations.<\/p>\n\n\n\n Some of this may be a review for you. Use this guide however is helpful for you. That may be skimming and double checking your understanding of the concepts we’ll cover, or it may be deep-diving into each topic. Let’s start with linear equations.<\/p>\n\n\n\n Linear equations<\/a> are the foundation of Algebra 1. When you start learning algebra and introducing variables into math, you start with linear equations. That’s because they are simple. They contain one variable and, when graphed, you get a straight line. <\/p>\n\n\n\n The reason linear equations<\/a> make straight lines when graphed is because they don\u2019t have exponents. No exponents mean we\u2019re always going to have a straight line.<\/p>\n\n\n\n On a real SAT, you\u2019ll likely find 2-4 questions that test how to solve linear equations. They could be:<\/p>\n\n\n\n This makes linear equations a frequently tested topic on the SAT. You should be able to identify linear equations and be able to consistently solve linear equations of both one and two variables.<\/p>\n\n\n\n We\u2019ll start with linear equations in one variable.<\/p>\n\n\n\n The key to solving linear equations<\/a> in one variable is isolating the variable. <\/strong> In other words, we want to get our variable all by itself. <\/p>\n\n\n\n Rule:<\/strong> Whenever you do something to one side of an equation, you must <\/em><\/strong>do it to the other side as well. <\/p>\n\n\n\n This rule is really important, especially as you tackle more complex linear equation questions. You don’t want to make simple mistakes on these questions.<\/p>\n\n\n\n Let’s look at an example.<\/p>\n\n\n\n Example 1:<\/span><\/strong> <\/p>\n\n\n\n If 6(x+2) -4 = 14, what is the value of x?<\/p>\n\n\n\n Ask yourself, \u201chow would you isolate x?\u201d<\/p>\n\n\n\n There are several paths you can take here, but I\u2019m always looking for the simplest (and fastest) path on the SAT. Don\u2019t waste any time!<\/p>\n\n\n\n Answer:<\/p>\n\n\n\n Start by adding 4 to both sides. Then, multiply out that 6 to both terms inside of the parentheses. <\/p>\n\n\n\n Great! We\u2019re getting closer. Now, let’s subtract the 12 from both sides.<\/p>\n\n\n\n Divide both sides by 6.<\/p>\n\n\n\n Example 2:<\/span><\/strong> <\/p>\n\n\n\n So far, we’ve been talking about equations, but the SAT does sometimes test expressions as well. The difference here is that expressions are groups of numbers and variables, but they do not contain an equals sign. Let’s go over an example.<\/p>\n\n\n\n In this question, we aren’t solving for x. We are asked which answer choice is equivalent to our given expression. In other words, which answer choice is equal to the given expression. It may not always be obvious where to start with these types of questions, but one option is to try to move some things around in your given expression and see if you start getting close to your answer choices.<\/p>\n\n\n\n Simplify if you can. In this case, combine 12 and -5<\/p>\n\n\n\n Does this match an answer choice? Yep!<\/p>\n\n\n\n Let\u2019s move on to linear equations in two variables<\/a>. If we have two variables (x and y), we need two equations in order to solve for x and y. If we have three variables (ex. a, b, c), we need three equations in order to solve for a, b and c.<\/p>\n\n\n\n You’ll see this concept tested in the form of systems of linear equations. Let’s look at an example.<\/p>\n\n\n\n Example 3:<\/span><\/strong> <\/p>\n\n\n\n There are two main ways to approach this question.<\/p>\n\n\n\n Approach 1:<\/strong><\/p>\n\n\n\n Plug in your answer choices into the system of equations. This is a good approach if you feel stuck. It may be more time consuming than Approach 2, but it can certainly work! <\/p>\n\n\n\n Tips: <\/p>\n\n\n\n Start with A and plug in (-2, -2). x = -2, y = -2.<\/p>\n\n\n\n -2 does not equal -4<\/p>\n\n\n\n We can eliminate A. <\/p>\n\n\n\n Try B and plug in (4, -2). x = 4, y = -2<\/p>\n\n\n\n 4 does not equal -4<\/p>\n\n\n\n We can eliminate B.<\/p>\n\n\n\n Try C and plug in (0, 2). x = 0, y = 2<\/p>\n\n\n\n Yes! 0 = 0. <\/p>\n\n\n\n It can be tempting to go with C and move on to the next question, but we have a bit more work to do. It’s possible that C only works for the first equation, so we need to test it on the second equation.<\/p>\n\n\n\n Awesome. Now we have our answer! If you are unsure, you can always test your remaining answer choices as well.<\/p>\n\n\n\n Approach 2:<\/strong><\/p>\n\n\n\n Instead of plugging in answer choices you can use either elimination or substitution to solve for x and y. In this case, substitution method works better. We actually already have x isolated in the first equation. Plug y – 2 in for x in the second equation and solve.<\/p>\n\n\n\n To get rid of the fraction, multiply everything by 2.<\/p>\n\n\n\n Combine like terms.<\/p>\n\n\n\n Divide by 5.<\/p>\n\n\n\n In this case we only have one answer choice with y = 2, so we have found our answer: C.<\/p>\n\n\n\n Have you ever thought about what the term \u201cinequality\u201d means? Inequality literally means \u201cnot equal,\u201d and that\u2019s exactly what\u2019s going on with mathematical linear inequalities. One side does not equal the other. Instead of an equal sign (=), we have greater than (>) or less than (<) signs to work with.<\/p>\n\n\n\n While linear equations<\/a> give us one distinct answer like x = 5, linear inequalities give us a range <\/em>of where our answer can be found.<\/p>\n\n\n\n To be able to solve linear inequalities on the SAT, you need to know the following inequality signs:<\/p>\n\n\n\n For the most part, you can treat linear inequalities <\/a>just like linear equations. Key word is most. <\/em>So, what\u2019s the exception? If we divide or multiply by a negative number, we have to flip the sign of the inequality.<\/p>\n\n\n\n Rule: <\/strong>Flip the sign when you multiply or divide by a negative number.<\/p>\n\n\n\n Let\u2019s look at an example.<\/p>\n\n\n\n Example 4:<\/span><\/strong><\/p>\n\n\n\n First, we should recognize this as a linear inequality equation because of the inequality sign (>) rather than an equal sign.<\/p>\n\n\n\n We\u2019re going to solve this just as we would solve a linear equation question: isolate x.<\/p>\n\n\n\n Add 3 to both sides.<\/p>\n\n\n\n Divide by 5.<\/p>\n\n\n\n We\u2019ve solved the linear inequality, but now we need to return back to our question and see what it\u2019s asking for.<\/p>\n\n\n\n It asks for a possible value.<\/strong> Because we are dealing with an inequality, x could be any number in a range <\/em>of values, and the SAT wants us to identify which answer choice is in that range. <\/em><\/p>\n\n\n\n Think to yourself: if x has to be greater than 2, what is one possible value that x could be? Any number that is greater than 2, so\u2026 3, 4, or 5.<\/p>\n\n\n\n At this point you would take a look at your answer choices and determine which one is greater than 2. Our answer will be D.<\/p>\n\n\n\n Nicely done.<\/p>\n\n\n\n Example 5:<\/span><\/strong> <\/p>\n\n\n\n This is a bit of a tricky question. It relies on your reasoning ability more than your ability to solve straightforward linear inequalities<\/a>. <\/p>\n\n\n\n You may notice that there’s a repeated expression (or part of an expression) in both inequalities. In the first inequality, we have 3x – 2 and in the second one, we have 3x. This is a good thing to notice. If we can get these two expressions to be exactly <\/em>equivalent, we can get to our answer. How? Let’s look at this another way. <\/p>\n\n\n\n What if the question said:<\/p>\n\n\n\n What would be the range of values of y that would satisfy the system of equations?<\/p>\n\n\n\n If y > K and K > 6, then it stands to reason that y > 6. This is relying on your logical reasoning skills. The more practice you do, the better you’ll get at recognizing these kinds of things.<\/p>\n\n\n\n Alright – now going back the question as it is written, you may start to see why I might want the 3x and 3x – 2 to be exactly <\/em>equivalent. I want to be able to do the kind of logic I was able to do with our magical variable K above.<\/p>\n\n\n\n What can we do to 3x to make it equivalent to 3x – 2? Subtract 2. If we subtract 2 from one side, we must also subtract 2 from the other side. So our second inequality becomes:<\/p>\n\n\n\n So, following our logic, we can say that y > 4. And, we have our answer: B.<\/p>\n\n\n\n SAT graphing linear equation questions <\/a>are all about using the y = mx + b formula. Look familiar? y = mx + b is the slope intercept form of a line. Remember: all linear equations, when graphed, are straight lines!<\/p>\n\n\n\n Let’s break down this formula.<\/p>\n\n\n\n In the slope intercept form of a line, m is the slope<\/strong>. The slope is how much a line rises or falls as it moves from left to right. In other words, slope is a measure of how steep a line is and if it’s going up (positive) or down (negative). Mathematically, slope can be represented as:<\/p>\n\n\n\n If we know any<\/em> two <\/em>points, we can calculate the slope of a line. As you get more comfortable with how expressions relate to their graphs, you’ll start to see how the slope of two lines can tell us about how the two lines are related. For the SAT, it’s important to know:<\/p>\n\n\n\n In the slope intercept form of a line, b <\/em>is the y-intercept<\/strong>. The y-intercept of a line is where the line crosses the y-axis. We’ve already learned how to make use of the y-intercept by translating it into a point. <\/p>\n\n\n\n The y-intercept, b, <\/em>is a constant – just like the slope, m.<\/em> While b <\/em>and m <\/em>can never change for a given line, we can infinite x and y values on that line.<\/p>\n\n\n\n The SAT wants to test your reasoning skills and how you navigate using this formula given various combinations of information to start with. It’s good to know that:<\/p>\n\n\n\n The point is: you need to identify what exactly you do <\/em>have when you start a problem, so you know how to work towards what you don’t <\/em>have. <\/p>\n\n\n\n Now that you understand what the m <\/em>and b <\/em>are in the slope intercept form of a line, y=mx+b, let’s look at how to make use of this on the SAT.<\/p>\n\n\n\n y = mx + b only works if the y is by itself, and thus, has a coefficient of 1. This is really important. If your line isn’t in correct form, you’re going to get the wrong answer.<\/p>\n\n\n\n Let’s look at an example.<\/p>\n\n\n\n Example 6:<\/span><\/strong><\/p>\n\n\n\n First things first. We need to get this line into the normal y=mx+b form. In order to do this, we want to isolate y. <\/p>\n\n\n\n Let’s subtract 3x from both sides. <\/p>\n\n\n\n Divide by -2.<\/p>\n\n\n\n We’re really close. It’s always a good idea to get into the exact <\/em>form of y = mx + b, so you don’t make any simple mistakes. We can do this by moving things around on the right side.<\/p>\n\n\n\n Great! Now we can see that our y intercept (b) is -4. <\/p>\n\n\n\n Trying to cram everything you need to know to ace the Heart of Algebra questions on the SAT Math sections? This is the tl;dr version if you’re short on time.<\/p>\n\n\n\n Kickstart Your SAT Prep with Test Geek’s Free SAT Study Guide. <\/a><\/h4>\n\n\n\n
Maximizing Your SAT Math Score – The Heart of Algebra<\/h2>\n\n\n\n
SAT Math Sections<\/h2>\n\n\n\n
![\"Two](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2021\/12\/heart-of-algebra-sat-1.png\")
<\/figure>\n\n\n\nWhat would 200 EXTRA POINTS do for you? Boost Your SAT Score with Test Geek SAT prep.<\/a><\/h4>\n\n\n\n
SAT Heart of Algebra<\/h2>\n\n\n\n
SAT Heart of Algebra: 7 Things You Need to Know<\/h3>\n\n\n\n
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<\/figure>\n\n\n\nLinear Equations<\/h2>\n\n\n\n
Linear Equations in One Variable<\/h3>\n\n\n\n
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<\/figure>\n\n\n\nLinear Equations in Two Variables<\/h2>\n\n\n\n
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<\/figure>\n\n\n\nLinear Inequalities<\/h2>\n\n\n\n
Feeling Overwhelmed? Get 1-on-1 SAT Help from a Test Geek Tuto<\/a><\/strong>r. <\/strong> <\/a><\/h4>\n\n\n\n
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<\/figure><\/div>\n\n\n\nLinear Inequalities in One Variable<\/h3>\n\n\n\n
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<\/figure><\/div>\n\n\n\nLinear Inequalities in Two Variables<\/h3>\n\n\n\n
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<\/figure>\n\n\n\nGraphing Linear Equations<\/h2>\n\n\n\n
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<\/figure>\n\n\n\nWhat would 200 EXTRA POINTS do for you? Boost Your SAT Score with Test Geek SAT prep.<\/a><\/h4>\n\n\n\n
![\"Group](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2021\/12\/heart-of-algebra-sat-3.png\")
<\/figure>\n\n\n\nHow to Use y = mx + b<\/h3>\n\n\n\n
![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2021\/12\/graphing-linear-equations-on-the-sat-10-1024x46.png\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2021\/12\/graphing-linear-equations-on-the-sat-11-1024x59.png\")
<\/figure>\n\n\n\n![\"\"](\"https:\/\/www.testgeek.com\/blog\/wp-content\/uploads\/2021\/12\/graphing-linear-equations-on-the-sat-12-1024x61.png\")
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<\/figure><\/div>\n\n\n\nRead This if You’re Short on Time<\/h2>\n\n\n\n